Editing General relativity (section)

=== Light deflection and gravitational time delay ===
{{Main|Schwarzschild geodesics|Kepler problem in general relativity|Gravitational lens|Shapiro delay}}
[[File:Light deflection.png|thumb|left|upright|Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)]]
General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a massive object. This effect was initially confirmed by observing the light of stars or distant quasars being deflected as it passes the [[Sun]].<ref>Cf. {{Harvnb|Kennefick|2005}} for the classic early measurements by Arthur Eddington's expeditions. For an overview of more recent measurements, see {{Harvnb|Ohanian|Ruffini|1994|loc=ch. 4.3}}. For the most precise direct modern observations using quasars, cf. {{Harvnb|Shapiro|Davis|Lebach|Gregory|2004}}</ref>

This and related predictions follow from the fact that light follows what is called a light-like or [[Geodesic (general relativity)|null geodesic]]—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the [[Invariant (mathematics)|invariance]] of lightspeed in special relativity.<ref>This is not an independent axiom; it can be derived from Einstein's equations and the Maxwell [[Lagrangian (field theory)|Lagrangian]] using a [[WKB approximation]], cf. {{Harvnb|Ehlers|1973|loc=sec. 5}}</ref> As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion),<ref>{{Harvnb|Blanchet|2006|loc=sec. 1.3}}</ref> several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light,<ref>{{Harvnb|Rindler|2001|loc=sec. 1.16}}; for the historical examples, {{Harvnb|Israel|1987|pp=202–204}}; in fact, Einstein published one such derivation as {{Harvnb|Einstein|1907}}. Such calculations tacitly assume that the geometry of space is [[Euclidean space|Euclidean]], cf. {{Harvnb|Ehlers|Rindler|1997}}</ref> the angle of deflection resulting from such calculations is only half the value given by general relativity.<ref>From the standpoint of Einstein's theory, these derivations take into account the effect of gravity on time, but not its consequences for the warping of space, cf. {{Harvnb|Rindler|2001|loc=sec. 11.11}}</ref>

Closely related to light deflection is the Shapiro Time Delay, the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.<ref>For the Sun's gravitational field using radar signals reflected from planets such as [[Venus]] and Mercury, cf. {{Harvnb|Shapiro|1964}}, {{Harvnb|Weinberg|1972|loc=ch. 8, sec. 7}}; for signals actively sent back by space probes ([[transponder]] measurements), cf. {{Harvnb|Bertotti|Iess|Tortora|2003}}; for an overview, see {{Harvnb|Ohanian|Ruffini|1994|loc=table 4.4 on p. 200}}; for more recent measurements using signals received from a [[pulsar]] that is part of a binary system, the gravitational field causing the time delay being that of the other pulsar, cf. {{Harvnb|Stairs|2003|loc=sec. 4.4}}</ref> In the [[parameterized post-Newtonian formalism]] (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.<ref>{{Harvnb|Will|1993|loc=sec. 7.1 and 7.2}}</ref>
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